16t^2-176t-160=0

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Solution for 16t^2-176t-160=0 equation: 


Simplifying
16t2 + -176t + -160 = 0

Reorder the terms:
-160 + -176t + 16t2 = 0

Solving
-160 + -176t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-10 + -11t + t2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(-10 + -11t + t2)' equal to zero and attempt to solve:

Simplifying
-10 + -11t + t2 = 0

Solving
-10 + -11t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -11t + 10 + t2 = 0 + 10

Reorder the terms:
-10 + 10 + -11t + t2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -11t + t2 = 0 + 10
-11t + t2 = 0 + 10

Combine like terms: 0 + 10 = 10
-11t + t2 = 10

The t term is -11t.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11t + 30.25 + t2 = 10 + 30.25

Reorder the terms:
30.25 + -11t + t2 = 10 + 30.25

Combine like terms: 10 + 30.25 = 40.25
30.25 + -11t + t2 = 40.25

Factor a perfect square on the left side:
(t + -5.5)(t + -5.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(t + -5.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
t + -5.5 = 6.34428877

Simplifying
t + -5.5 = 6.34428877

Reorder the terms:
-5.5 + t = 6.34428877

Solving
-5.5 + t = 6.34428877

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '5.5' to each side of the equation.
-5.5 + 5.5 + t = 6.34428877 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + t = 6.34428877 + 5.5
t = 6.34428877 + 5.5

Combine like terms: 6.34428877 + 5.5 = 11.84428877
t = 11.84428877

Simplifying
t = 11.84428877


Subproblem 2
t + -5.5 = -6.34428877

Simplifying
t + -5.5 = -6.34428877

Reorder the terms:
-5.5 + t = -6.34428877

Solving
-5.5 + t = -6.34428877

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '5.5' to each side of the equation.
-5.5 + 5.5 + t = -6.34428877 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + t = -6.34428877 + 5.5
t = -6.34428877 + 5.5

Combine like terms: -6.34428877 + 5.5 = -0.84428877
t = -0.84428877

Simplifying
t = -0.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.84428877, -0.84428877}
Solution
t = {11.84428877, -0.84428877}

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